The pictorial presentation of surfaces of a tubular object with a complicated shape, such as the bronchial system, a vascular system or other hollow organs, forms the basis for a plurality of analyses, especially in the clinical field. Numerous problems can be detected for example with the aid of a fly-through of the hollow organ, the simulation of the course of a fluid or the more detailed three-dimensional presentation of critical areas, so that a further procedure can be defined especially in relation to the medical treatment. This requires that the most complete information possible about the topological structure of the tubular object is available. Such information about the topological structure can be obtained for example with the aid of imaging methods, such as computed tomography or magnetic resonance tomography for example. Without further processing the images and presentations thus obtained are only suitable to a limited extent or not suitable at all for the analyses. The multidimensional description of the surface of the hollow organ with the aid of a boundary surface network presentation or surface network modeling, abbreviated hereafter to “boundary surface network”, delivers the desired geometrical information and for the above analyses should also reproduce details of the surface to a sufficient extent.
Methods are known for calculating a boundary surface network of a hollow organ in precise detail, which describe the surface with the aid of numerically complicated and computing-intensive interpolations. The calculated boundary surface networks are generally characterized by an outstanding level of accurate detail. Because the enormous computing effort involved however, these presentations cannot be calculated within a short time or instantaneously, so that real-time manipulations, for example for “what if” analyses, in order to simulate the insertion of a stent into a blood vessel for example, only enter into consideration to a limited extent on the basis of these methods for calculating a boundary surface network.
The necessary speed in the determining of the boundary surface network can be achieved by simplifying the numerical effort with the aid of a model of the surface that is as simple as possible. By contrast with “model-free” interpolation computation methods which are based on the analysis of point clouds, such models approximate the hollow organ of which an image is to be produced with the aid of a set of simple geometrical shapes such as cylinders or spheres for example. This approximation however only rarely delivers a boundary surface network of the hollow organ which reproduces critical details, especially in the area of branching points, approximately correctly. As a result of this an exact dimensioning of geometrical changes of the vascular system is unsuitable for diagnosis and treatment planning of a pathology.
For simulation of a course of the fluid it is for example necessary for the entire geometry and especially branches of the hollow organ to be reproduced as identically as possible to their natural state, and above and beyond this the boundary surface network calculated should frequently be “watertight”, i.e. it may not feature any openings which are not present in reality.
Results of the model-based determination of a boundary surface network only rarely meet these requirements however, since especially the adaptation of the simple geometrical basic form is complicated when the size conditions of part structures of the hollow organ vary greatly and when branches occur. Undesired artifacts in the boundary surface network determined occur at branches as a result of simple geometrical basic model elements such as spheres or the like frequently used for modeling projecting into each other and structures which are not present in reality are modeled in the interior of the boundary surface network determined. These boundary surface networks are for example only usable to a restricted extent for the said “fly-through” applications.